The options you mention are not a part of the theme’s native functionality, but are rather easy to achieve:
1). to have the actual-size background image in the top center position on the page, please download this custom template file, unzip it, and upload via ftp into the theme’s folder (wp-content/themes/Fuji), replacing the existing file.
2). the easiest and most feature-rich plugin that enables setting different backgrounds for each individual page (and even background sliders) is WP Supersized; I highly recommend it and have been using it myself for a long time. Please note that the background created using this plugin will not be positioned as in the first point, i.e. will still stretch the entire screen.
In case this does not fully solve the problem or I can be of any other help, do tell! :)
I’ve installed the WP Supersized plugin – and replaced the header as you instructed – but the supersized header image I’ve specified is not displaying. Here are my WP Supersized settings (http://screencast.com/t/Lg7QIxMyCI) and here are my theme settings (http://screencast.com/t/eXeVDvT8) do I need to change something in the Theme Options to allow the WP Supersized plugin to work?
I do not see the Supersized code on the page you provided – have you deactivated the plugin? I have used WP Supersized with Fuji multiple times and there seems to be no problems with the plugin compatibility. If the issue is still topical, could you please send me the admin login and password to firstname.lastname@example.org (no disclosure guaranteed) – this way I will be able to troubleshoot and fix the problem quicker and more efficiently.